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Elasticity Models

The behavior of a material is said to be elastic when its displacement is linearly proportional to the applied load, and returns to its undeformed state when the load is removed.

For elastic materials, stress is directly proportional to the strain as indicated by:

{σ} = [D] {ε - εt}

[D] = elastic (isotropic, anisotropic, or orthotropic) material or material stiffness matrix

{σ} = the total stress vector

{ε} = the total strain vector

t} = thermal strain vector

The above rule is an approximation that is valid as long as the strains are small for certain types of materials. The above equation is known as constitutive relation. While they take this simple form for linear elastic materials, the constitutive relations can be quite complex for nonlinear materials.

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